This is pretty simple. At first sign in to your Blogger account and create a new page and copy the page URL in your clipboard.
Then go to Google Custom Search engine page and sign in with your Google Account.
Click the link that says New Search Engine.
Now add your blog URL (http:// is optional) and Create new search engine. Now expand Edit Search Engine from left pane and go to Look and Feel.

Now select Two Page and don’t forget to press the Save button each time after making any kind of change. From here, you can change the theme, color etc.
After doing everything, click on Save & Get Code. Now press the button, which says Search Results Details. Here you have to paste the page URL what you have made in your blogger account (in the first step).
Now the current page will show you some lines of code for Search box. Copy them and paste them where you would like to show the search box. I prefer sidebar-above-fold.
Now go to the next page and copy all the lines of code and paste them in the search result page in your blogger account. Make sure that you are on HTML view.
Now save your changes.
Check my one here.